As for non-aqueous electrolyte secondary batteries such as lithium-ion secondary batteries, studies have been conducted to further improve the battery performance (e.g. higher capacities, greater recyclability). As a technology related to this, for instance, Patent Document 1 discloses a non-aqueous secondary battery that has a lithium transition metal composite oxide comprising manganese and tungsten in the positive electrode and further includes boehmite (alumina hydrate) between the positive and negative electrodes.